# The Deviation of the Vacuum Refractive Index Induced by a Static Gravitational Field

## TL;DR

This paper derives an analytical expression for how a static gravitational field causes inhomogeneity in the vacuum's refractive index, explaining gravitational lensing effects through effects like time dilation and length contraction.

## Contribution

It introduces the concept of inhomogeneous vacuum and provides a new analytical model for vacuum's refractive index in gravitational fields, linking it to observable light deflection.

## Key findings

- Refractive index deviation has two components: time dilation and length contraction.
- The model explains the missing central image in gravitational lensing.
- Simulation results support the inhomogeneous vacuum concept.

## Abstract

We analyzed the influence of static gravitational field on the vacuum and proposed the concept of inhomogeneous vacuum. According to the observational result of the light deflection in solar gravitational field as well as the corresponding Fermat's principle in the general relativity, we derived an analytical expression of the refractive index of vacuum in a static gravitational field. We found that the deviation of the vacuum refractive index is composed of two parts: one is caused by the time dilation effect, the other is caused by the length contraction effect. As an application, we simulated the effect of the gravitational lensing through computer programming and found that the missing central imaging could be interpreted in a reasonable way.